Method and apparatus for the measurement and indication of the position of a coiled material in tape form

ABSTRACT

The position of the tape in a magnetic tape recorder is obtained by counting the pulses derived from the revolutions of a reel or spool. The ratio of the number of revolutions per minute of the reels and the total number of turns is determined by means of a test run; the counting process is linearized by means of these values.

BACKGROUND OF THE INVENTION

The position or setting of tapes in magnetic tape recorders can bedetermined by the counting of pulses which are derived from a partmoving together with the magnetic tape such as, for example, thespindles. The number counted may be employed for indicating the tapesetting. Since the length of the circumference of a tape reel varieswith the coiling or uncoiling of the magnetic tapes this indication isnot linear. That is, considerably varying values are obtained for thetape section assigned to individual counting steps as a function of thetape setting.

With a view towards improving the linearity of indication it has beenproposed (German Auslegeschrift No. 24 16 060.9) to provide a scanningunit on each of the two spindles, to derive tape travelling pulses fromthe scanning units and to feed the sum of the pulses into a counter.While this method effects some improvement in indication it is in somecases still inadequate in effecting an improvement in linearity such as,for example, when the indication has to be calibrated to the length oftape which has been run dimensionally.

SUMMARY OF THE INVENTION

An object of the invention is to provide a method for indicating thetape setting which is greatly improved with respect to linearity as aresult of which it becomes possible to perform an absolute calibrationin meters or seconds.

In the course of the determination of the tape setting in a magnetictape recorder by means of the counting of pulses derived typically fromthe take-up spindle; the changing reel diameters during the coilingoperation produce a non-linear counting result over the tape length. Incommercially available magnetic tape cassettes the length of play of agiven cassette is a function of the tape length and different thicknesstapes are used as a function of the tape length.

The invention is based on the finding that the variables affecting thewinding operation which have to be allowed in the linearisation of thecounting operation can be expressed by two values which can be easilydetermined during a test run of the magnetic tape recorder concerned.These are

1. The ratio of the diameter of the fully wound reel to the diameter ofthe empty hub of a reel and

2. The total number of turns (winding number) of a full reel.

One series of pulses each is derived from each of the two spindles forthe detection of these values. The first value is determined by afrequency comparison of the pulse series during a test run from thestarting setting of the magnetic tape at which the take-up reel is emptyand the take-off reel is full. The second value is derived by a count ofthe pulses making up one of the pulse series over the full tape lengthor a part of the tape length. In the described embodiment the pulses arecounted by the take-up spindle.

Assuming that the diameters of the hubs of the take-up and take-offreels are identical the tape setting can be derived with these values bymeans of the following formula ##EQU1##

The various symbols in this formula have the following meanings: L isthe tape setting, a figure which varies linearly with the length of tapedelivered which figure may be indicated (reported) through applicationof an appropriate factor in a length unit, for example meters, or in atimeunit such as minutes. D₀ is the diameter of the hubs of the reels,N₁ the appropriate number of turns on the take-up reel, N_(1ges) thepossible total number of turns, and a the frequency ratio of the pulseseries derived from the take-up and take-off reels at the start of thewinding process.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block circuit diagram of the invention.

FIGS. 2 and 3 are circuit units relating to the circuit of FIG. 1.

FIG. 4 is a variant of the circuit of FIG. 3.

FIG. 5 is an embodiment of a frequency comparator provided in thecircuit of FIG. 2.

FIG. 6 is a table relating to the circuit of FIG. 5.

FIG. 7 shows pulse diagrams relating to the circuit of FIG. 5.

DESCRIPTION OF A PREFERRED EMBODIMENT

FIG. 1 shows part of a magnetic tape cassette apparatus with twospindles 1 and 2 between which a magnetic tape 3 can be arbitrarilymoved to and fro. The diagram only shows the outer circumferences of themagnetic tape reels which change with the tape setting or position. Inthe illustrated case the reel on the left is fully wound and the reel onthe right is empty. Pulses are generated through the travel of the tape.Marks 8 are provided for this purpose on the spindles 1 and 2 or someother part moving in unison with the reels such as the drive shaft forthe spindles 1 and 2. Pulse pick-ups 6 and 7 are provided for scanningthese marks 8. At the outputs of the pulse pick-ups 6 and 7 arise pulseseries 16 and 17 respectively when the magnetic tape is running. At theindicated tape setting the pulse series 16 has the lowest occurringpulse repetition frequency and the pulse series 17 the the highestoccurring pulse repetition frequency because the circumferences of thereels have in one case the largest and in the other case the smallestoccurring diameter.

The pulse pick-up 7 is wired to a counter 12 in which the pulses 17 arecounted commencing from the beginning of the tape. Since the frequencyof the pulse series 17 varies with the length of tape moved the countersetting does not vary linearly with the tape position. A correction istherefore applied to the counting result in a correction circuit 13. Thecorrected counting result from the output of the correction circuit isindicated in an indicating unit 14 and is transmitted to a controlcircuit 15. This control circuit 15 is employed for the control of thefunctions of the magnetic tape recording apparatus, it thus beingpossible to provide an automatic setting facility to a desired tapesetting which is introduced through an input keyboard. In such anautomatic setting run the read-in desired tape setting is comparedagainst the actually determined value. The travel of the magnetic tapeis controlled so that the two values are made to coincide. Appropriatecircuits for this are already known.

A mathematical correction calculation in accordance with the aforesaidformula based on the geometrical laws of the tape reeling process iscarried out in the correction circuit 13. In this context L is themeasuring result giving the tape setting available at the output of thecorrection circuit 13, and N₁ is the counter setting of the counter 12corresponding to the number of revolutions of the spindle 1. N_(1ges) isthe number of turns of a full magnetic tape reel; that is, a reel whichhas been fully loaded with tape. The variable a-1 included in theformula is determined in the case of the circuit per FIG. 1 in block 10.A test run of the magnetic tape is made from the indicated startingsetting to determine and store in block 10 the frequency ratio of thepulse series 16 and 17 and this is fed through a lead 18 to thecorrection circuit 13. From a run through of the magnetic tape isdetermined and stored the variable N_(1ges) in the block 11 and this ispassed from there through the lead 19 to the correction circuit 13. Thetotal number of turns N_(1ges) may also be determined by a run up to themiddle of the magnetic tape, in which case the sameness of thefrequencies of the pulse series 16 and 17 can be employed as aswitching-off criterion.

N_(1ges) and a are two values which clearly designate the magnetic tapecassette employed and are therefore determined once after the insertionof a cassette or after switching on the apparatus and are stored for aslong as an apparatus uses this magnetic tape. In order to obtain alinear tape setting indication it is therefore necessary to first carryout the described procedure in which the values of N_(1ges) and a aredetermined while the magnetic tape is running.

FIG. 2 is an example of an embodiment of the circuits of the blocks 10,11 and 12 described in connection with FIG. 1. The pulses from thespindles of the magnetic tape recorder are fed through input terminals21 and 23 to pulse forming circuits 22 and 24. The block 10 comprises apreprogrammable counter 29. An addition constant -m applied to an input34 of the counter 29 is introduced into the counter 29 through astarting pulse at the input L of the counter 29. The pulses from thespindles 1 are fed to the input of counter 29 through a gate 25. Thegate 25 is open for the time of m pulses coming from the spindle 2. Acounter 27 and a 1-memory 28 are provided for the control of the gate25. The counter 27 is brought to its starting setting by the alreadypreviously mentioned starting pulse which brings the 1-bit memory 28into a state at which the logic state "1" exists at the output Q. Thegate 25 is controlled with the output signal from the 1-bit memory 28.The gate 25 may, for example, be in the form of an AND-gate with twoinputs, whereby the pulses are fed into one input and the other input isconnected with the output of the 1-bit memory 28. On occurrence of thestarting pulse at the input terminal 35 into the entire circuit the gate25 is opened and is closed again after the receipt of m pulses from thespindle 2 because then the memory 28 takes over a logic "1"corresponding to "0" at the output Q. After this opening time thesetting of the counter 29 is m (a-1) whereby a is the frequency ratio ofthe pulse series 17 derived from the spindle 1 in FIG. 1 and the pulseseries 16 derived from the spindle 2. When the value m is a dual number,and the divider 27 is hence a dual divider (m) this value can be easilyeliminated through division by a numeral value m corresponding to aplace shift (comma shift). The counter setting of the counter 29 istransmitted through the lead 18 to a yet be described correction circuit13 in FIG. 1.

The pulses from the spindle 1 are passed via a divider 30 with thedividing ratio of 1:n to the input of the counter 12. For theimprovement of the accuracy of the values determined in block 10 thenumber of pulses derived from the spindle is selected to have so large avalue that only every nth pulse need be counted in the counter 12. Onthe assumption that the dividing factor n corresponds to the number ofmarks p on the spindles the setting of the counter 12 will just indicatethe number of revolutions N₁ of the spindle.

Block 11 comprises a frequency comparator 31 and a memory 32. The numberof memory steps of the memory 32 equals the number of counting steps ofthe counter 12. The output of the counter 12 is connected with the inputinto the memory 32. The memory 32 together with the counter 12 areerased by the starting pulse at the input terminal 35 of the circuit.The counter setting of the counter 12 can be transferred into the memory32 through a loading pulse at the input L of the memory 32. The input Lof the memory 32 is connected with the output of the frequencycomparator 31. At the input of the frequency comparator are applied thefrequencies f₁ and f₂ of the pulse series derived from the spindles. Thefrequencies f₁ and f₂ are equal when the reel diameters are of equalmagnitude indicating that the middle of the tape has been reached. Atthis point a loading signal is put into the input L into the memory 32.This loading signal causes the reading in and storage in the memory 32of the counter setting of the counter 12 which equals exactly half ofthe maximum total number of turns (N_(1ges))/ 2. The reading in of thecounter setting into the memory 32 completes the storage of all valuesneeded for the correction of the tape setting indication. The loadingsignal at the input L of the memory 32 serves therefore at the same timeas a stop command for the control circuit 15 in FIG. 1. It can be takenoff the output terminal 36. The starting pulse at the input 35 isgenerated only once when a new cassette is inserted or the apparatus isswitched on. The starting signal may be typically triggered off by theinsertion of a cassette.

After the test run of the magnetic tape recorder has been completed itis possible to run the counter 12 arbitrarily forwards and backwards asa function of the direction of travel of the magnetic tape. During thebackwards travel the counter 12 receives on one input Abw through aninput terminal 33 an opposite direction information signal from thecontrol circuit designated by 15 in FIG. 1 as a result of which thedirection of counting of the counter 12 is reversed.

When the tape setting indicator has to be returned to zero at a givenpoint in time, e.g. at the start of the tape, after the test run hasbeen completed, it is only the counters 12 and 48 (FIG. 3) but not thecounters 29 and the memory 32 which may be reset. The stored valueswould otherwise be lost. The resetting may be effected throughadditional reset inputs of the counters 12 and 48 through a signal whichdiffers from the starting pulse.

The signals shown in FIG. 2 on the right hand margin are transferred tothe correction circuit (13 in FIG. 1) shown in FIG. 3.

The correction circuit comprises a circuit 37 for the squaring of thecounting pulses at the input of the counter 12 in FIG. 2, also adividing circuit 43 for dividing by the value N_(1ges), a multiplier 44for the multiplication with the value a-1 and a summer 45 for adding thevalue N₁ to the output of multiplier 44.

The squaring circuit 37 comprises a 1-bit memory 40, a counter 38, acomparator 39 and a gate 41. A signal with a constant relatively highfrequency of typically 1 MHz is fed from an oscillator, not shown,through an input terminal 42 to the counter 38 and the input of the gate41. The output Q of the 1-bit memory 40 is wired to the reset input R ofthe counter 38. The input Z1 of the comparator 39 is wired to the outputof the counter 38 and the output of the counter 12 in FIG. 2 isconnected with another input Z2 of the comparator 39. The countingpulses are fed to the loading input L of the memory 40. The output ofthe comparator 39 is wired to the reset input R of the memory 40. Thelogic state "1" is transferred into the memory 40 on occurrence of acounting pulse so that a signal "0" is available at its output Q. As aresult of the connection of the output Q with the reset input R of thecounter 38 this latter counter 38 is thereby switched to be ready forcounting. Through a connection from the output Q of the memory 40 to thegate 41 the gate 41 is opened simultaneously so that the constantfrequency pulses are allowed to pass through the gate 41. When thecounter setting of the counter 38 is the same as the counter setting N₁of the counter 12 in FIG. 2 a reset signal is passed from the comparator39 to the reset input R of the memory 40. The counter 38 is as a resultreset and the gate 41 is closed. The described procedure is started anewby the next counting pulse at the input L of the memory 40.

The number of constant frequency pulses allowed by the gate 41 to passat every counting pulse increases with the increase of the countersetting N₁ of the counter 12. At the output of the gate 41 appear pulsestacks, the number of pulses of which increases linearly with the valueN₁. The pulses are counted in a counter 48 in block 43. The result ofthe count corresponds to the sum formula of an arithmetic series asfollows:

    =N.sub.1 ·(1+N.sub.1 /2)=N.sub.1 /2+N.sub.1.sup.2 /2

Since the square portion (N₁ ² /2) predominates it is possible todisregard the portion N₁ /2.

On the supply side of the counter 48 is inserted a programmable divider47 the programming input of which is connected with the output of thememory 32 in FIG. 2. A circuit 46 for forming the complement of thevalue held in memory 32 may be inserted depending on the configurationof the programmable divider 47 employed.

The dividing ratio of the programmable divider 47 is determined by thevalue N_(1ges/) 2. The pulse number is divided in this way so that thecounter setting of the counter 48 gives the value N₁ ² /N_(1ges).

The output of the counter 48 is wired to the input of the multiplier 44.The other input is wired through the lead 18 to the output of thecounter 29 in FIG. 2. The output of the multiplier 44 is wired to theinput of the summer 45. The other input of the summer 45 is at theoutput of the counter 12 in FIG. 2. At the output of the summer 45appears a value which varies linearly with the length of tape passed andwhich is employed for the tape setting indication and control of FIG. 1.

Corresponding to the counter 12 in FIG. 2 the counter 48 in block 43 isreset by the previously mentioned starting pulse into its startingsetting and its direction of counting can be reversed by the previouslyreferred to direction reversed signal. The circuit blocks used in FIGS.2 and 3 are prior art type standard modules employed in digital computerengineering. The multiplier 44 may typically consist of the prior artintegrated circuits SN 74284 made by Texas Instruments and the summer 45may consist of the integrated circuit SN 74283 made by the samemanufacturer. These must always be used in cascade arrangement.

The above described circuit is an example of an embodiment for thecarrying out of the method in accordance with the invention. The circuitmay be varied in many ways without thereby changing the method fordetermining the tape setting. The multiplier 44 in FIG. 4 for examplemay be replaced by a programmable divider which is placed on the inputside of the counter 48. The value (a-1) would then have to be replacedby its reciprocal 1/(a-1) which would be fed into the programmabledivider. This reciprocal may be obtained by reversing the two inputsignals of circuit 10.

In the case of the circuit per FIGS. 2 and 3 it is necessary to firstrestore the magnetic tape into its starting setting after completion ofthe test run for the determination of the values a and N_(1ges). Onstandard playing operation of the magnetic tape apparatus a new count isthen started which will be subject to the correction controlled by thestored values. Normal operation cannot be started from the setting atwhich the test run was completed because counting in the counter 48(FIG. 3) depends upon the value N_(1ges). This value is not yetavailable during the test run.

FIG. 4 shows a circuit which is varied from the circuit of FIG. 3 inthat it is possible to take up normal operation directly after the testrun. All parts in this circuit corresponding to parts in the circuit ofFIG. 3 bear the same reference symbols. The pulses coming forward fromthe gate 41 in the square-law transfer element 37 are first counted inthe counter 48' and are only then divided by the value N_(1ges) /2 inthe divider 49. The content of the counter 48 is a result not dependentupon the values determined during the test run, so that the correctionmay be still applied after completion of the test run. This circuitcorresponds in all other respects to the circuit of FIG. 3. The dividermay be made up of a combination of prior art integrated circuits inaccordance with page 235 in the "TTL" cookery book" published by TexasInstrument, 1973.

The divider 49, the multiplier 44 and the summer 45 in FIG. 4 may becombined into a calucating register. This also applies to the blocks 44and 45 in FIG. 3. The square-law transfer element 37 could also beincluded in such registers. In the case of the circuit of FIG. 4 it isalso possible to start the test run from the middle of the tape. In thisthe magnetic tape is first brought into this setting in which case thestop command is taken from the comparator 31. The value N_(1ges) /2 isdetermined by a test run to the beginning or end of the magnetic tapeand followed by the determination of the value a at the end or thebeginning of the magnetic tape.

The method explained with the aid of FIGS. 1 to 4 greatly improves thelinearity of the tape setting indication. The tape setting can beindicated either directly in meters (tape length) or in minutes (theplaying time corresponding to the tape length). In the latter case thereexists the advantage that the length of a recorded piece can be directlyread off from the readings of the start and end of this piece.

The above described circuit for the implementation of the method isbeneficially made in the form of an integrated circuit.

The frequency comparator 31 in FIG. 2 must be suitable for thecomparison of low frequencies. It is therefore advantageous to conduct acomparison of the two pulse series which extends over several periods.FIG. 5 shows a suitable circuit for this which will be described in thefollowing. The pulse series (16 and 17 in FIG. 1) with the frequenciesf₁ and f₂ derived from the spindles are fed in through input terminals61 and 62. The pulses with the frequency f₁ are fed in to the input of aBCD divider 50 and pulses with the frequency f₂ into the input of anidentical divider 52. The four outputs from the BCD divider aredesignated A, B, C and D. At the output D of the dividers 50 and 52 thelogical signal "0" appears during the settings zero to seven of thedividers 50 and 52. From the output D of the divider 50 is triggeredthrough an inverter 59 a gate 53 and correspondingly from the divider 52through an inverter 60 a gate 55. The gates 53 and 55 are, for example,designed in the form of and gates with two inputs. The output of theinverters 59 and 60 are connected with the respective control inputs ofthe relevant gates. A pulse signal with a constant frequency f₃occurring at an input terminal 64 is fed to the other inputs of thegates 53 and 55. The output of the gate 53 is wired to the countinginput of a counter 54 and the output of the gate 55 to the countinginput of a counter 56.

The outputs of the counters 54 and 56 are wired to the comparison inputsof a comparator 57. At the output of the comparator 57 appears thelogical signal "1" when the counter settings of the counters 54 and 56are equal. Excepted from this are however the counter setting of zero.Such a comparator 57 can be easily built up from logical gates. Theoutput of the comparator 57 and the outputs D of the dividers 50 and 52are linked through an AND-gate 58. The output of the AND-gate 58 iswired to an output terminal 63 which forms the output of the frequencycomparator 31. A gate 51 is connected to the outputs A, B, C and D ofthe divider 50 so that the logical signal "1" is given off at the outputof the gate 51 when the countersetting of the divider 50 is nine. Aconnection shown as a broken line between the gate 51 and the input ofthe divider 50 assures that the logical state at the output of the gateis obtained directly upon the reaching of the counter setting nine andonly for the duration of the ninth pulse. The pulse produced at theoutput of the gate 51 is designated in the following by the term "resetpulse". The gate 51 may, for example, be in the form of an AND-gate withthree inputs of which one input is connected with the output A, anotherwith the output D and the third input with the input of the divider 50.The output of the gate 51 is connected with a setting input of thedivider 52 with which the divider 52 can be changed into the settingnine and is also connected with reset inputs R of the counters 54 and56.

The circuit works as follows: Let it be assumed that the startingsetting of the dividers 50 and 52 is nine. From the spindle 1 (see FIG.1 and 3) pulses are counted into the divider 50 through the inputterminal 61. The gate 53 is first opened so that pulses with constantfrequency f₃ can be counted into the counter 54. The gate 53 is closedwith the ninth counting pulse of the divider 50. The setting of thecounter 54 after the closing of the gate 53 represents the duration of 8periods of frequency f₁.

Nine pulses are correspondingly counted in from the spindle 2 throughthe input terminal 62 into the divider 52. The gate 55 is again open forthe duration of eight counting pulses of the divider 53. The countersetting on the counter 56 achieved after this time represents the lengthof 8 periods with the frequency f₂ derived from the spindle 2. Thefrequencies f₁ and f₂ will coincide when the counter settings of thecounters 54 and 56 are the same after a counting period. In this casethere appears at the output terminal 63 the logic signal "1" since allinputs of the AND gate 58 are set at logic "1". The frequency f₃ is, forexample, 100 KHz. The magnitude of the frequency governs the accuracy ofthe frequency comparator. On attainment of the setting nine by thedivider 50 the divider 52 will be set into its starting setting nine bythe previously mentioned reset pulse. The counters 54 and 56 are resetat the same time too. The described counting process starts afresh. Itis continuously periodically repeated.

FIG. 6 shows a table, which gives the logical signals at the inputs andthe outputs of the AND-gate 58 at various relationships of thefrequencies f₁ and f₂ to one another. All inputs of the AND-gate 58 arein the logical state "1" only in the event of frequency sameness. Thesignals shown in brackets apply to an example shown in FIG. 7. They mayhowever also adopt the contrary logical state under certain conditions.

FIG. 7 shows a pulse diagram for the circuit of FIG. 5. The first tworows show the pulse series with frequencies f₁ and f₂. Below these areshown the counting periods of the counter 54 which reach from thesetting zero to the setting eight of the divider 50. The reset pulsesfor resetting the divider 52 and the counters 54 and 56 shown in thefourth row are generated with the ninth pulse of the pulse series f₁.The counting time of the counter 56 is for both possible cases offrequency sameness greater than the counting period of the counter 54,as can be seen from the next two rows. In the case of frequency samenessin the bottom line of FIG. 7 the counting period of the counter 56equals exactly that of counter 54. This means, that the counters 54 and56 count equal numbers of pulses of frequency f₃ and that the logicalsignal "1" occurs at the comparator 57.

The counting capacity of the dividers 50 and 52 is advantageously pickedto correspond with the number of marks or a whole number multiple of thenumber of marks so that the start and end of the counting periods of thecounter 54 and 56 are always determined by the same marking. Thiseffects compensation of the tolerances in the gaps between the marks.

It is possible to block the gates 53 and 55 during several intermediatestates of the divider 50 to permit reducing of the counting capacity ofthe counters 54 and 56. This could be typically done from state twountil state six. Only the differences at the begin and the end of thecounting periods will in this case be detected. The parts of noimportance for the comparison is blanked out.

The circuit described with the aid of FIG. 5 represents a specificexample. The circuit can be adapted in detail to the requirements givenby the application case. It is, for example, possible to pick thecounting capacity of the dividers 50 and 52 and of the counters 54 and56 differently. It is also possible to vary the periodic course of thefunction, for example, by a different wiring of the gate 51.

The described method may also be employed for other wound material intape form such as films which are moved between two reels.

I claim:
 1. Apparatus for indicating the position of a tape wound onfirst and second reels and movable therebetween, comprising:pulsegenerating means coupled to said first and second reels for generatingfirst and second pulse trains having pulse repetition frequenciescorresponding to the angular speeds of said first and second reels,respectively; frequency ratio means for determining the ratio a of thepulse repetition frequency of said first pulse train to the pulserepetition frequency of said second pulse train, said determinationbeing made when one of said reels has substantially no tape woundthereon; turns counting means for determining the maximum total numberof turns N_(1ges) of tape on one of said reels when said reel iscompletely loaded; pulse counting means coupled to said pulse generatingmeans for counting the number of accumulated pulses N₁ in said firstpulse train starting from the beginning of the winding of said tape onsaid first reel; and correction circuit means coupled to the outputs ofsaid frequency ratio means, turns counting means and pulse countingmeans, the output of said correction circuit means corresponding to theposition L of the tape on said first reel.
 2. Apparatus as defined byclaim 1 wherein the diameters of the hubs of said first and second reelsare equal, and wherein said ratio a, total number of turns N_(1ges) andthe number of accumulated pulses N₁ are related by the formula ##EQU2##where k is a constant calibration factor.
 3. Apparatus as defined byclaim 1 wherein said frequency ratio means comprises:a presettable firstcounter having an input and an output; a controllable gate having aninput terminal coupled to said pulse generating means to receive one ofsaid first and second pulse trains, an output coupled to the input ofsaid first counter, and a control input; and a second counter having aninput terminal coupled to said pulse generating means to receive theother of said first and second pulse trains and an output coupled to thecontrol input of said gate, said gate being open for settings between 0and a value m of said second counter, said first counter beingpresettable to said value m, and said first and second counters beingpreset and reset, respectively, by a starting pulse applied thereto. 4.Apparatus as defined by claim 1 wherein said turns counting meanscomprises:a memory circuit having a first input coupled to the output ofsaid pulse counting means, said memory circuit having a number ofstorage steps corresponding to the number of counting steps of saidpulse counting means; a frequency comparator having a first inputterminal coupled to said pulse generating means to receive one of saidfirst and second pulse trains and a second input terminal coupled tosaid pulse generating means to receive the other of said first andsecond pulse trains, the output of said frequency comparator beingcoupled to a second input terminal of said memory, said memory circuitinitiating storage of the output of said pulse counting means when thefrequencies of the first and second pulse trains applied to the firstand second input terminals of said frequency comparator are equal; andmeans for applying a starting pulse to said pulse counting means andsaid memory circuit for erasing the contents thereof.
 5. Apparatus asdefined by claim 4 wherein said correction circuit means includes asquaring circuit comprising:a counter having a first input adapted forcoupling to a constant frequency pulse source; a comparator having afirst input coupled to the output of said counter and a second inputcoupled to the output of said pulse counting means; a 1-bit memoryhaving a first input for receiving counting pulses and a second inputcoupled to the output of said comparator, said 1-bit memory having anoutput coupled to a second input of said counter for the resettingthereof; and a gate having an output, a first input adapted for couplingto said constant frequency pulse source and a second input coupled tothe output of said 1-bit memory, said counter being reset by the outputof said 1-bit memory and said gate closed when the signals applied tothe first and second inputs of said comparator are the same, an outputcorresponding to the square of the pulse numbers of the counting pulseapplied to the first input of said 1-bit memory being generated at theoutput of said gate.
 6. Apparatus as defined by claim 5 which furthercomprises:a programmable divider having a first input coupled to theoutput of said gate and a second input coupled to the output of saidmemory circuit; and a second counter coupled to the output of saidprogrammable divider.
 7. Apparatus as defined by claim 6 wherein saidpulse counting means and said second counter are reversible with respectto the direction of travel of said tape.
 8. Apparatus as defined byclaim 5 which further comprises:a second counter having an input coupledto the output of said gate; and a dividing circuit having a dividendinput coupled to the output of said second counter and a divisor inputcoupled to the output of said memory circuit.
 9. Apparatus as defined byclaim 1 wherein said correction circuit means includes a squaringcircuit comprising:a counter having a first input adapted for couplingto a constant frequency pulse source; a comparator having a first inputcoupled to the output of said counter and a second input coupled to theoutput of said pulse counting means; a 1-bit memory having a first inputfor receiving counting pulses and a second input coupled to the outputof said comparator, said 1-bit memory having an output coupled to asecond input of said counter for the resetting thereof; and a gatehaving an output, a first input adapted for coupling to said constantfrequency pulse source and a second input coupled to the output of said1-bit memory, said counter being reset by the output of said 1-bitmemory and said gate closed when the signals applied to the first andsecond inputs of said comparator are the same, an output correspondingto the square of the pulse numbers of the counting pulse applied to thefirst input of said 1-bit memory being generated at the output of saidgate.
 10. Apparatus as defined by claim 1 wherein said frequency ratiomeans comprises:a presettable first counter having an input and anoutput; a controllable gate having an input terminal coupled to saidpulse generating means to receive one of said first and second pulsetrains, an output coupled to the input of said first counter and acontrol input; and a second counter having an input terminal coupled tosaid pulse generating means to receive the other of said first andsecond pulse trains and an output coupled to the control input of saidgate, said gate being open for settings between 0 and a value m of saidsecond counter, said first counter being presettable to a value m, andsaid first and second counters being preset and reset, respectively, bya starting pulse applied thereto, and wherein said turns counting meanscomprises:a memory circuit having a first input coupled to the output ofsaid pulse counting means, said memory circuit having a number ofstorage steps corresponding to the number of counting steps of saidpulse counting means; a frequency comparator having a first inputterminal coupled to said pulse generating means to receive one of saidfirst and second pulse trains and a second input terminal coupled tosaid pulse generating means to receive the other of said first andsecond pulse trains, the output of said frequency comparator beingcoupled to a second input terminal of said memory, said memory circuitinitiating storage of the output of said pulse counting means when thefrequencies of the first and second pulse trains applied to the firstand second input terminals of said frequency comparator are equal; andmeans for applying a starting pulse to said pulse counting means andsaid memory circuit for erasing the contents thereof.
 11. Apparatus asdefined by claim 10 which further comprises:a programmable dividerhaving a first input coupled to the output of said gate and a secondinput coupled to the output of said memory circuit; a third countercoupled to the output of said programmable divider; a multiplier havinga first input coupled to the output of said third counter and a secondinput coupled to the output of said presettable first counter; and asummer having a first input coupled to the output of said multiplier anda second input to the output of said pulse counting means, the output ofsaid summer corresponding to the position of the tape on said firstreel.
 12. Apparatus as defined by claim 10 which further comprises:athird counter having an input coupled to the output of said gate; adividing circuit having a dividend input coupled to the output of saidthird counter and a divisor input coupled to the output of said memorycircuit; a multiplier having a first input coupled to the output of saiddividing circuit and a second input coupled to the output of saidpresettable first counter; and a summer having a first input coupled tothe output of said multiplier and a second input to the output of saidpulse counting means, the output of said summer corresponding to theposition of the tape wound on said first reel.
 13. A method formeasuring the position of a tape wound on first and second reels andmovable therebetween, said reels being provided with means forgenerating first and second pulse trains having pulse repetitionfrequencies corresponding to the angular speeds of said first and secondreels, respectively, comprising the steps of:determining the ratio a ofthe pulse repetition frequency of said first pulse train to the pulserepetition frequency of said second pulse train when one of said reelshas substantially no tape wound thereon; determining the maximum totalnumber of turns N_(1ges) of tape on one of said reels when said reel iscompletely loaded; counting the number of accumulated pulses N₁ in saidfirst pulse train starting from the beginning of the winding of saidtape on said first reel; and computing the position L of said tape onsaid first reel from the formula ##EQU3## where k is a constantcalibration factor.
 14. The method defined by claim 13 wherein the ratioa and number of turns N_(1ges) are determined for reels having hubs ofequal diameters by a test run comprising the steps of:winding all ofsaid tape on said second reel; beginning to wind the tape from saidsecond reel to said first reel; dividing the pulse repetition frequencyof said first pulse train by the pulse repetition frequency of saidsecond pulse train at the beginning of said winding operation to obtainthe ratio a thereof; continuing to wind the tape from said second reelto said first reel until the pulse repetition frequency of said firstpulse train is equal to the pulse repetition frequency of said secondpulse train, the winding of said tape being terminated at this point;and counting the number of pulses in said first pulse train, said numberbeing equal to one-half the number of turns N_(1ges).